MADISON, Wis. — The arc of science has faced roadblocks for centuries, but the pattern of denying the weight of evidence has taken on new virulence recently. Highly motivated people openly cast doubt on well-established evidence — the theory of evolution, the human effects on climate change, the value of vaccines and other findings that have achieved an overwhelming consensus in the scientific community.

Researchers and science writers tasked with reporting on these issues gathered April 2...